Highest Common Factor of 624, 896, 30 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 624, 896, 30 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 624, 896, 30 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 624, 896, 30 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 624, 896, 30 is 2.
HCF(624, 896, 30) = 2
HCF of 624, 896, 30 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 624, 896, 30 is 2.
Highest Common Factor of 624,896,30 is 2
Step 1: Since 896 > 624, we apply the division lemma to 896 and 624, to get
896 = 624 x 1 + 272
Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 272 and 624, to get
624 = 272 x 2 + 80
Step 3: We consider the new divisor 272 and the new remainder 80, and apply the division lemma to get
272 = 80 x 3 + 32
We consider the new divisor 80 and the new remainder 32,and apply the division lemma to get
80 = 32 x 2 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 624 and 896 is 16
Notice that 16 = HCF(32,16) = HCF(80,32) = HCF(272,80) = HCF(624,272) = HCF(896,624) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 16, we apply the division lemma to 30 and 16, to get
30 = 16 x 1 + 14
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 14 and 16, to get
16 = 14 x 1 + 2
Step 3: We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 30 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) .
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Frequently Asked Questions on HCF of 624, 896, 30 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 624, 896, 30?
Answer: HCF of 624, 896, 30 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 624, 896, 30 using Euclid's Algorithm?
Answer: For arbitrary numbers 624, 896, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.